Stellar Production Rates of Carbon and Its Abundance in the Universe

Abstract

Abstract:The bulk of the carbon in our universe is produced in the triple-alpha process in helium-burning red giant stars. We calculated the change of the triple-alpha reaction rate in a microscopic 12-nucleon model of the 12 C nucleus and looked for the effects of minimal variations of the strengths of the underlying interactions. Stellar model calculations were performed with the alternative reaction rates. Here, we show that outside a narrow window of 0.5 and 4 % of the values of the strong and Coulomb forces, respectively, the stellar production of carbon or oxygen is reduced by factors of 30 to 1000. The formation of12 C through the triple-alpha process takes place in two sequential steps in the He-burning phase of red giants. In the first step, the unstable 8 Be with a lifetime of only about 10 −16 s is formed in a reaction equilibrium with the two alpha particles, α + α ⇀ ↽ 8 Be. In the second step, an additional alpha particle is captured, 8 Be(α, γ) 12 C. Without a suitable resonance in 12 C, the triple-alpha rate would be much too small to account for the 12 C abundance in our universe. Hoyle (1) suggested that a resonance level in 12 C, at about 300-400 keV above the three-alpha threshold, would enhance the triple-alpha reaction rate and would explain the abundance of 12 C in our universe. Such a level was subsequently found experimentally when a resonance that possessed the required properties was discovered (2, 3). It is the second 0 + state in 12 C, denoted by 0 + 2 . Its modern parameters (4) are ε = (379.47 ± 0.18) keV, Γ = (8.3 ± 1) eV, and Γ γ = (3.7 ± 0.5) meV, where ε is the resonance energy in the center-of-mass frame relative to the three-alpha threshold, and Γ and Γ γ are the total width and radiative width, respectively.The isotope 12 C is synthesized further in the He burning in red giants by alpha capture to the O isotope 16 O, leading to an abundance ratio in the universe of 12 C : 16 O ≈ 1 : 2 (5). If the carbon abundance in the universe were suppressed by orders of magnitude, no carbon-based life could have developed in the universe. But the production of O is also necessary because no spontaneous development of carbon-based life is possible without the existence of water.Here, we investigated the abundance ratios of C and O by starting from slight variations of the strength of the nucleon-nucleon (N-N) interaction with a microscopic 12-nucleon model. In previous studies, only hypothetical ad hoc shifts of the resonance energy of the 0 + 2 state were considered (6). Some preliminary results of our cal-1

Effects of the variation of fundamental constants on Population III stellar evolution

“…The direct effect of δ α is thus of opposite sign but considerably less important. This is in qualitative agreement with Oberhummer et al (2000) and Oberhummer et al (2001). It is appropriate at this point to further note that within the limits of variation in δ NN that we are considering here, the effect on promoting the stability of dineutron or diproton states is negligible.…”

“…where T 9 = T/10 9 K. This effect was investigated by Csótó et al (2001) and Oberhummer et al (2000Oberhummer et al ( , 2003 who related the variation in Q ααα to a variation in the strength of the nucleonnucleon (N-N) interaction. Focusing on the C/O ratio in red giant stars up to thermally pulsing asymptotic giant branch stars (Oberhummer et al 2000(Oberhummer et al , 2003 and in low, intermediate and high mass stars (Schlattl et al 2004) at solar metallicity, it was estimated that outside a window of 0.5% and 4% for the values of the strong and electromagnetic forces respectively, the stellar production of carbon or oxygen will be reduced by a factor 30 to 1000 (see also Pochet et al 1991).…”

“…Focusing on the C/O ratio in red giant stars up to thermally pulsing asymptotic giant branch stars (Oberhummer et al 2000(Oberhummer et al , 2003 and in low, intermediate and high mass stars (Schlattl et al 2004) at solar metallicity, it was estimated that outside a window of 0.5% and 4% for the values of the strong and electromagnetic forces respectively, the stellar production of carbon or oxygen will be reduced by a factor 30 to 1000 (see also Pochet et al 1991). Indeed, modifying the energy of the resonance alone is not realistic since all cross-sections, reaction rates and binding energies etc.…”

“…Rozental' (1988) argued that the synthesis of complex elements in stars (mainly the possibility of the triple α reaction (3α) as the origin of the production of 12 C) sets constraints on the values of the fine structure and strong coupling constants. There have been several studies on the sensitivity of carbon production to the underlying nuclear rates (Barrow 1987;Livio et al 1989;Fairbairn 1999;Csótó et al 2001;Oberhummer et al 2000Oberhummer et al , 2003Schlattl et al 2004;Tur et al 2007). The production of 12 C in stars requires a triple tuning: (i) the decay lifetime of 8 Be, of order 10 −16 s, is four orders of magnitude longer than the time for two α particles to scatter; (ii) an excited state of the carbon lies just above the energy of 8 Be + α and finally (iii) the energy level of 16 O at 7.1197 MeV is non resonant and below the energy of 12 C + α, at 7.1616 MeV, which ensures that most of the carbon synthesised is not destroyed by the capture of an α-particle.…”

Three's a Crowd: On Causes, Entropy and Physical Eschatology

“…The most promising one lies in arguing that there are physical reasons-offered by the theory of inflation-why the creation of very small (in cosmological terms) low-entropy domain is impossible or very improbable, and that events taking place only in large universes (like the formation of the large-scale structure and the process galaxy formation) are causally linked to our appearance as intelligent observers. As far as astrophysics is concerned, prospects for such a resolution are rather good, since it seems that both nucleosynthesis of elements heavier than lithium and the formation of terrestrial planets are dependent on these "grand stage" processes (Hogan 2000;Oberhummer et al 2000). In other words, not all types of universes are created out of chaotic inflation (thus we are deviating from Boltzmann's possibility of "all natural events... without restriction"), but they belong predominantly to two types: ones with very large entropy throughout and ones with very low entropy.…”